12年级微积分和向量（MCV4U） | Xiaominlaoshi

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MCV4U - Limits & Derivatives - Properties of Limits & Examples

24:44

MCV4U - Limits & Derivatives - Properties of Limits & Examples

MCV4U - Limits & Derivatives - Product Rule

17:37

MCV4U - Limits & Derivatives - Product Rule

MCV4U - Limits & Derivatives - Quotient Rule

23:18

MCV4U - Limits & Derivatives - Quotient Rule

MCV4U - Limits & Derivatives - Rate of Change

22:18

MCV4U - Limits & Derivatives - Rate of Change

Revisiting Rate of Change of a function, from the MHF4U Advanced Functions course, in terms of the limit definition. Allows us to come up with exact expressions and values for RoC.

MCV4U - Limits & Derivatives - One Sided Limits

19:05

MCV4U - Limits & Derivatives - One Sided Limits

MCV4U - Limits & Derivatives - Chain Rule

16:20

MCV4U - Limits & Derivatives - Chain Rule

MCV4U - Limits & Derivatives - Continuity

17:17

MCV4U - Limits & Derivatives - Continuity

MCV4U - Limits & Derivatives - Rationalizing Radicals

15:10

MCV4U - Limits & Derivatives - Rationalizing Radicals

Rationalizing radical terms in both numerator and denominator of a rational expression.

MCV4U - Optimization - Optimize Money v2

35:23

MCV4U - Optimization - Optimize Money v2

I created this video with the YouTube Video Editor (http://www.youtube.com/editor)

MCV4U - Optimization - Optimizing Time

27:02

MCV4U - Optimization - Optimizing Time

MCV4U - Optimization - Optimizing Distance Exercises

21:49

MCV4U - Optimization - Optimizing Distance Exercises

MCV4U - Optimization - Optimizing Distance

21:07

MCV4U - Optimization - Optimizing Distance

MCV4U - Optimization - Optimization Problems

20:07

MCV4U - Optimization - Optimization Problems

MCV4U - Optimization - Extreme Values

19:04

MCV4U - Optimization - Extreme Values

MCV4U - Optimization - Higher Order Derivatives

25:30

MCV4U - Optimization - Higher Order Derivatives

MCV4U - Curve Sketching - Geogebra Demo Relate Function to Derivatives

22:21

MCV4U - Curve Sketching - Geogebra Demo Relate Function to Derivatives

This video is a supplement to the lessons on curve sketching using calculus, specifically focusing on the first and second derivative test.

MCV4U - Curve Sketching - Concavity & Points of Inflection

22:50

MCV4U - Curve Sketching - Concavity & Points of Inflection

Supplemental demo using Geogebra: https://youtu.be/3E0asjSMxCg This lesson looks at how to use the second derivative to locate possible critical values and classify them as extrema or points of inflection using concavity (i.e., the second derivative test).

MCV4U - Curve Sketching - Oblique Asymptotes

16:33

MCV4U - Curve Sketching - Oblique Asymptotes

MCV4U - Curve Sketching - Asymptotes

23:56

MCV4U - Curve Sketching - Asymptotes

MCV4U - Curve Sketching - Critical Points

28:13

MCV4U - Curve Sketching - Critical Points

MCV4U Curve Sketching - Intervals of Increase & Decrease

31:25

MCV4U Curve Sketching - Intervals of Increase & Decrease

MCV4U - Derivative of Tangent Function

12:45

MCV4U - Derivative of Tangent Function

Shows the derivative of the tangent function starting from the sin/cos definition, and then examples making use of the chain rule.

MCV4U - Derivatives of Sine & Cosine

22:10

MCV4U - Derivatives of Sine & Cosine

MCV4U Optimization & Curve Sketching of Exponential Functions

28:04

MCV4U Optimization & Curve Sketching of Exponential Functions

Jump to: 2:56 Start of exercise, derivatives 9:25 Solve for critical values 14:51 Classify using 2nd derivative test 20:39 End behaviour using limits 23:58 Sketch

MCV4U - Derivatives of Logarithms

26:54

MCV4U - Derivatives of Logarithms

Demonstration, but not proof, of derivative of natural logarithm (lnx), and then extension to general logarithmic functions.

MCV4U - Deriviatives of General Exponential Functions

20:35

MCV4U - Deriviatives of General Exponential Functions

The derivative of any exponential function in the form b^x, making use of the natural logarithm, ln(x).

MCV4U -Derivatives of the Natural Exponential Function

27:02

MCV4U -Derivatives of the Natural Exponential Function

13:25 Jump to main lesson & examples Development of the natural number, 'e', in the context of a derivative of an exponential function.

MCV4U - Linear Combinations & Spanning Sets

22:49

MCV4U - Linear Combinations & Spanning Sets

MCV4U - Algebraic Vector Operations in R3

12:54

MCV4U - Algebraic Vector Operations in R3

MCV4U - Algebraic Vector Operations in R2

32:11

MCV4U - Algebraic Vector Operations in R2

MCV4U - Vectors in R3

17:48

MCV4U - Vectors in R3

MCV4U - Vectors in R2

15:20

MCV4U - Vectors in R2

MCV4U - Scalar Multiplication of a Vector

26:55

MCV4U - Scalar Multiplication of a Vector

MCV4U Vectors 02 - Adding & Subtracting Vectors

19:30

MCV4U Vectors 02 - Adding & Subtracting Vectors

Vector addition and vector subtraction.

MCV4U Vectors 01 - Introduction to Vectors

06:28

MCV4U Vectors 01 - Introduction to Vectors

MCV4U - Applications Dot Cross Product

22:17

MCV4U - Applications Dot Cross Product

A very superficial treatment of applications of dot and cross product. From physics, we look at a simple example of work (dot product) and torque (cross product).

MCV4U - Cross Product

25:13

MCV4U - Cross Product

MCV4U - Vector Projections

25:19

MCV4U - Vector Projections

MCV4U - Dot Product of Algebraic Vectors

14:58

MCV4U - Dot Product of Algebraic Vectors

MCV4U - Dot Product of Geometric Vectors

19:20

MCV4U - Dot Product of Geometric Vectors

MCV4U - Velocity Vectors

22:00

MCV4U - Velocity Vectors

MCV4U - Vectors as Forces - Exercises

39:02

MCV4U - Vectors as Forces - Exercises

A supplemental video to the lesson on Vectors as Forces. This video is way too long, and I make a couple of silly mistakes (which I thankfully catch, but still). Apologies to anybody who tries to watch it.

MCV4U - Applications of Vectors - Forces as Vectors

17:44

MCV4U - Applications of Vectors - Forces as Vectors

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MCV4U - Distance between Points Lines Planes in R3

13:12

MCV4U - Distance between Points Lines Planes in R3

Formulas are provided for: R2: Point to Line R3: Point to Line R3: Point to Plane Other cases can be reduced to one of the above: R2: Two parallel lines R3: Two parallel lines R3: Two parallel planes R3: Parallel line and plane R3: Skew (non-parallel, non-intersecting) lines

MCV4U - Intersection of Three Planes

24:04

MCV4U - Intersection of Three Planes

Three planes can be represented as a system of three equations in three unknowns. The various possible results are explored in this lesson.

MCV4U - Solving Systems of Equations Using Matrices

23:04

MCV4U - Solving Systems of Equations Using Matrices

A matrix (plural matrices) can be used as an alternate algebraic mechanical technique for solving a system of equations. This lesson focuses on three equations and three unknowns, but it scales upwards very easily.

MCV4U - Intersections of Two Planes

18:39

MCV4U - Intersections of Two Planes

Two planes in R3 can intersect along a line (infinite solutions) or along the entire plane (same plane, infinite solutions). The two planes can also be parallel but distinct (no solutions).

MCV4U - Intersection of Lines and Planes

18:54

MCV4U - Intersection of Lines and Planes

MCV4U - Intersection of Lines in R3

24:51

MCV4U - Intersection of Lines in R3

MCV4U - Cartesian Equation of a Plane in R3

27:26

MCV4U - Cartesian Equation of a Plane in R3

MCV4U - Vector Equation of Plane

25:41

MCV4U - Vector Equation of Plane

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